F(x)=-x+5/2x-1

Solution for F(x)=-x+5/2x-1 equation:

(F)=-F+5/2F-1

We move all terms to the left:

(F)-(-F+5/2F-1)=0


Domain of the equation: 2F-1)!=0

F∈R


We add all the numbers together, and all the variables

F-(-1F+5/2F-1)=0

We get rid of parentheses

F+1F-5/2F+1=0

We multiply all the terms by the denominator


F*2F+1F*2F+1*2F-5=0

Wy multiply elements

2F^2+2F^2+2F-5=0

We add all the numbers together, and all the variables

4F^2+2F-5=0

a = 4; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·4·(-5)
Δ = 84
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{21}}{2*4}=\frac{-2-2\sqrt{21}}{8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{21}}{2*4}=\frac{-2+2\sqrt{21}}{8}
$